Hi, I have donated to a milk bank before and it was a good experience for me. Our milk bank is only an hour away and they did "local pickup" in my city - I just had to drop off the frozen milk to a nurse's office and the bank would come retrieve it.
It wasn't hard to get approved, but it was time consuming. I had to fill out a lot of paperwork and send it in - then when the paperwork was approved, I was told to get blood drawn. Then it took another week or two before the blood sample was analyzed and they could start accepting my milk. They would take any milk I had pumped prior to the blood draw, so your freezer stash would still be ok to donate.
Since your milk bank is farther away, I'm not sure how they would manage shipping. I hope they would send you prepaid containers or set something up with FedEx, but I don't know for sure. Give them a call and ask - that part is free!